Please help me solve this problem

Handwritten Problems You *MUST* show your work and use proper notation for full credit. 1. As part of a study of natural variation in blood chemistry, serum potassium concentrations were measured in 66 randomly selected healthy women. The sample mean concentration was 4.36 mEq/1, and the sample standard deviation was 0.42 mEq/1. (a) Find the 95% confidence interval for the true serum potassium concentrate in healthy women. (b) Interpret your confidence interval in terms of the problem. (c) Does your interval support the claim that normal serum potassium concentrations are above 2.3? Explain why or why not. (d) How many women would you need in the study to ensure a margin of error for your 95% confidence interval of 0.05? (e) If we were to build a 99% confidence interval instead, would it widen or narrow? Explain why. (f) A large prior study found that serum potassium concentrate in healthy women was on average 4.4 mEq/1. State the null and alternative hypotheses using proper notation testing if your data supports this claim or not at the 95% confidence interval. (g) Based on the hypothesis test above, calculate the test-statistic, showing your formula and the values that you plug in. (h) Based on the hypothesis test above, find the appropriate critical value, compare it to your test statistic, and state your decision to reject or fail to reject Ho (do not worry about context here). (i) Based on the hypothesis test above, calculate the p-value. (j) Compare your p-value to alpha and state your decision to reject or fail to reject Ho (do not worry about context here). (k) Your confidence interval, hypothesis test, and p-value should all have reached the same decision to reject or fail to reject Ho. Clearly state your decision in the context of the problem, i.e. using the words of the problem. (1) Sketch a t distribution, label your test statistic, label the critical value, shade the region(s) for the appropriate alpha, shade the region(s) for the appropriate p-value. Does your picture make sense when you compare it to your decisions above